Find three different irrational numbers between the rational numb… - Vidyadip

Question

Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}.$

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Answer

$\frac{5}{7}=0.\overline{714285}$ $\frac{9}{11}=0.\overline{81}$ $3$ irrational numbers are- $0.73073007300073000073... 0.75075007500075000075... 0.790790079000790000...$
Concept Insight: There is infinite number of rational and irrational numbers between any two rational numbers.
Convert the number into its decimal form to find irrationals between them.
Alternatively following result can be used to answer: Irrational number between two numbers $x$ and $y$
$=\sqrt{\text{xy}},$ if $x$ and $y$ both are irrational numbers $=\sqrt{\text{xy}},$ if x is rational number and $y$ is irrational number $=\sqrt{\text{xy}},$ if $x × y$ is not a perfect square and $x, y$ both are rational numbers

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